Elastic Boides,. 177 



m (u u') n (u 1 i>)j 



m u m u' = n u' nu, 

 we obtain 



7 _ m w + nu 

 m+fi 5 



therefore, tu/ien the bodies move in the same direction, in order to find, 

 the velocity after collision, we take the, sum of the quantities of motion, 

 which the bodies had before collision, and divide this sum by the sum 

 of the masses. 



Thus, if m, for example, be equal to 5 ounces and n to 7, it 

 equal to 8 feet in a second, and v to 4 feet in a second, we shall 

 have, 



5x8+7x4 40 + 28 

 5 + 7 ~l2~~ 



that is, the velocity after collision will be five feet and two thirds 

 in a second. 



288. If one of the two bodies, as n for example, were at rest 

 before collision, we should have v = 0, and the expression of 

 the velocity after collision would accordingly become 



mu 

 m + n ' 



that is, we should divide the quantity of motion belonging to the 

 impinging body by the sum of the masses of the two bodies. 



If, however, instead of deducing this case from the more gen- 

 eral one, we would find it directly, we should proceed according 

 to the same principles, and consider the impinged body as hav- 

 ing, in consequence of the collision, a velocity u', equal to and 

 in the direction of that which it is to have after collision, and a ve- 

 locity u', of the same magnitude, but in the opposite direction. 

 Thus, since it is to preserve only the first, it is necessary that in 

 virtue of the second it should be in equilibrium with the body m, 

 having a velocity u u' which it is to lose. Accordingly we 

 must have 



Mech. 23 



